What do you know about these three guys?
s(t) - Position
v(t) - Velocity
a(t) - Acceleration
????
That is their usual names, anyway.
Derivative move down the list. Antiderivative move up. Which do you need.
Can someone help explain how to do this problem?
Pizza Delivery Problem: Ida Livermore starts off on her route. She records her truck's speed, v(t), in mi/hr, at various times, t, in seconds, since she started.
v(t)=5t^(½)
Approximately how far did Ida's truck travel from t=1 to t=9?
I don't understand why find the derivative.
It should be integration.
V(t) is in mi/hr, while t is in seconds. And the book answer is in feet.
The units don't tally.
Convert mi/hr into ft/sec.
(1mi/1hr)(5280ft/1mi)(1hr/3600sec) = (5280)/(3600) = 1.4667 ft/sec
So the
V(t) in mph = 5*t^(1/2)
should be
V(t) in ft/sec = (5*1.4667)t^(1/2)
S = (5*1.4667)INT.(1-->9)[t^(1/2)]dt
S = (7.333)(2/3)[t^(3/2)]|(1-->9)
S = (4.888)[9^(3/2) -1^(3/2)]
S = (4.888)[27 -1]
S = 127.088
or
S = 127 ft.